📚 A Deep Dive into Year 7 Cambridge Maths Past Papers | 剑桥7年级数学历年真题深度解析
Preparing for Year 7 Cambridge Mathematics assessments requires more than just knowing formulas—it demands the ability to apply concepts to unfamiliar problems, spot common traps, and manage time effectively. Analysing past papers is one of the most powerful revision strategies. This guide takes you through real past paper questions, breaking down solutions step by step, highlighting typical errors, and sharing examiner insights that will boost your confidence and score.
备考剑桥7年级数学考试，不仅需要牢记公式，更需要将概念应用到陌生题目中、识别常见陷阱并有效管理时间。分析历年真题是最有效的复习策略之一。本指南将带你走进真实的历年考题，逐步拆解解题过程，指出典型错误，并分享考官视角的洞察，助你提升信心和分数。
1. Working with Negative Numbers | 负数的运算
Example Question: Calculate –15 + 8 – (–6)
例题： 计算 –15 + 8 – (–6)
Step 1: Deal with the double negative. – (–6) becomes +6, so the expression simplifies to –15 + 8 + 6. Step 2: Add –15 + 8 to get –7. Then –7 + 6 = –1. Always work from left to right when only addition and subtraction are involved.
步骤一：处理双重负号。– (–6) 变为 +6，因此表达式简化为 –15 + 8 + 6。步骤二：–15 + 8 = –7，然后 –7 + 6 = –1。当只有加减法时，务必从左到右依次计算。
Common mistake: Many students forget to change the sign when subtracting a negative number, ending up with –15 + 8 – 6 = –13, which is incorrect.
常见错误：许多学生减去负数时忘记变号，算成 –15 + 8 – 6 = –13，导致错误。
Exam tip: Always circle any negative signs in front of brackets before starting your calculation to avoid careless slips.
考试提示：开始计算前，用笔圈出括号前的负号，避免粗心犯错。
2. Fractions in Context | 分数应用题
Example Question: A fruit basket has 36 pieces. John takes 2/9 of them and Mary takes 1/4. How many pieces remain?
例题：一个水果篮有36个水果。约翰拿走其中的2/9，玛丽拿走1/4。还剩下多少个？
hn takes: 2/9 × 36 = 8. Mary takes: 1/4 × 36 = 9. Total taken = 8 + 9 = 17. Remaining = 36 – 17 = 19 pieces.
计算约翰拿走的数量：2/9 × 36 = 8。玛丽拿走的数量：1/4 × 36 = 9。一共拿走 8 + 9 = 17。剩余 36 – 17 = 19 个水果。
and subtract. This method is also correct but ensure you subtract the amount, not just leave it as a fraction of the basket.
考官视角：有些学生先加分数：2/9 + 1/4 = 8/36 + 9/36 = 17/36，再计算 17/36 × 36 = 17，然后相减。此方法也正确，但一定要记得求出具体数量后再做减法，不能只停留在分数上。
Always check that your final answer makes sense in the context—if more than half are taken, the remainder should be less than half.
始终检查答案在上下文中是否合理——如果取走了一大半，剩余数量应少于总数的一半。
3. Decimal Operations and Rounding | 小数运算与四舍五入
Example Question: Multiply 0.45 by 0.8 and give your answer to two decimal places.
例题：计算 0.45 × 0.8，并将答案保留两位小数。
aces, so 0.45 × 0.8 = 0.360, which is 0.36. Rounded to two decimal places it remains 0.36.
先忽略小数点：45 × 8 = 360。原数字共有 2 + 1 = 3 位小数，因此 0.45 × 0.8 = 0.360，即 0.36。保留两位小数为 0.36。
Common pitfall: Forgetting to count total decimal places correctly, writing the answer as 3.6 or 0.036. Always tally decimal places after multiplying the whole numbers.
常见陷阱：忘记正确计算小数总位数，答案写成 3.6 或 0.036。务必在整数相乘后重新计算小数位数。
For rounding, if the third decimal place is 5 or more, round up. In this case, 0.360 has 0 in the third place, so no change.
关于四舍五入，如果第三位小数≥5，则进位。本例中 0.360 第三位是0，因此不变。
4. Introduction to Algebra | 代数入门
Example Question: Simplify 4x + 3y – 2x + y – x
例题：化简 4x + 3y – 2x + y – x
Group like terms: x‑terms: 4x – 2x – x = (4 – 2 – 1)x = 1x = x. y‑terms: 3y + y = 4y. Simplified expression is x + 4y.
合并同类项：含 x 的项：4x – 2x – x = (4 – 2 – 1)x = 1x = x。含 y 的项：3y + y = 4y。化简结果为 x + 4y。
Many students incorrectly write 1x + 4y, which loses the mark for not fully simplifying. 1x is simply written as x.
不少学生错写成 1x + 4y，因为没有彻底化简，1x 应直接写作 x。
Remember: only like terms can be combined—you cannot add 4x and 3y together because the variables are different.
记住：只有同类项才能合并——不能将 4x 和 3y 加在一起，因为字母不同。
5. Solving Simple Equations | 解简单方程
Example Question: Solve 5p – 3 = 2p + 9
例题：解方程 5p – 3 = 2p + 9
Step 1: Collect the p‑terms on one side by subtracting 2p from both sides: 5p – 2p – 3 = 9 → 3p – 3 = 9. Step 2: Add 3 to both sides: 3p = 12. Step 3: Divide by 3: p = 4.
步骤一：将含 p 项移到一边，两边同时减 2p：5p – 2p – 3 = 9 → 3p – 3 = 9。步骤二：两边加 3：3p = 12。步骤三：两边除以 3，得 p = 4。
Common error: Forgetting to perform the same operation on both sides, such as adding 3 only to the left side. Always maintain balance.
常见错误：忘记两边同时进行相同操作，例如只给左边加 3。务必保持等式平衡。
Check your answer by substituting back: 5(4) – 3 = 20 – 3 = 17; 2(4) + 9 = 8 + 9 = 17. It works!
把答案代回原方程检验：5×4 – 3 = 17；2×4 + 9 = 17。两边相等，答案正确。
6. Angle Properties of Triangles | 三角形的内角特性
Example Question: In triangle ABC, ∠A = 58° and ∠B = 3x – 10°. Angle C is right‑angled. Find the value of x.
例题：在三角形 ABC 中，∠A = 58°，∠B = 3x – 10°，∠C 为直角。求 x 的值。
Sum of angles in a triangle is 180°, and a right angle is 90°. So, 58 + (3x – 10) + 90 = 180. Simplify: 58 + 90 – 10 = 138, giving 138 + 3x = 180. Subtract 138: 3x = 42. Divide by 3: x = 14.
三角形内角和为 180°，直角为 90°。因此 58 + (3x – 10) + 90 = 180。化简：58 + 90 – 10 = 138，于是 138 + 3x = 180。两边减 138：3x = 42。除以 3，得 x = 14。
Many candidates forget that a right angle equals 90° and try to use 100° or ignore it entirely. Always highlight the keyword ‘right‑angled’.
许多考生忘记直角等于90°，误用 100° 或完全忽略。务必圈出关键词“直角”。
Once x is found, check the angles: 3×14 – 10 = 32°. Then 58 + 32 + 90 = 180, confirming the answer.
得出 x 后检验角度：3×14 – 10 = 32°，然后 58 + 32 + 90 = 180°，验证无误。
7. Perimeter of Compound Shapes | 组合图形的周长
Example Question: The shape is made from a rectangle and a right‑angled triangle. The rectangle measures 5 cm by 3 cm. The triangle shares the 3 cm side, and its other leg is 4 cm. Find the perimeter of the whole shape.
例题：下图由一个矩形和一个直角三角形组成。矩形长5 cm、宽3 cm。三角形与矩形共用3 cm的边，其另一直角边为4 cm。求整个图形的周长。
ngth 5 cm. Triangle shares the 3 cm side, so its base 4 cm is horizontal. The hypotenuse = √3² + 4² ngle top) + 4 + 5 (hypotenuse) = 22 cm. The shared 3 cm side is not part of the perimeter.
画出图形：矩形高3 cm，长5 cm。三角形共用3 cm边，其底边长4 cm。斜边 = √3² + 4² = 5 cm。周长 = 所有外边界：5 + 3 + 5（矩形顶边）+ 4 + 5（斜边）= 22 cm。共用的3 cm边不计入周长。
Common mistake: Including the shared interior side in the perimeter, double‑counting it, or forgetting to find the hypotenuse and leaving a gap.
常见错误：将内部共用边计入周长、重复计算，或忘记求斜边而留下缺口。
Always trace the outside boundary with your finger and write down the lengths in order to avoid missing a side.
用手沿着外边界描一圈，按顺序写下各边长度，以防漏掉某条边。
8. Interpreting Bar Charts and Pictograms | 解读条形图和象形图
Example Question: The bar chart shows the number of books read by five students. Ali read 12, Bella 8, Chen 15, Devi 10 and Eva 5. What percentage of the total books was read by Chen?
例题：条形图显示五位学生的阅读书本数量：Ali 12本，Bella 8本，Chen 15本，Devi 10本，Eva 5本。Chen 阅读的书占总数的百分之几？
Total books = 12 + 8 + 15 + 10 + 5 = 50. Chen’s share = 15/50 = 3/10 = 30/100 = 30%. Answer: 30%.
总数 = 12 + 8 + 15 + 10 + 5 = 50 本。Chen 的份额 = 15/50 = 3/10 = 30/100 = 30%。答案：30%。
In pictograms, check the key thoroughly. A frequent error is misreading the symbol’s value, e.g., assuming one book symbol equals 1 instead of 2. Always multiply correctly.
在象形图中，仔细查看图例。常见错误是误读符号的值，例如假设一个书本符号代表1本而实际代表2本。务必正确相乘。
When calculating percentages, simplify the fraction first to reduce errors, and always check that the percentage is reasonable (not over 100%).
计算百分比时，先约分可减少错误，并检查百分比是否合理（不应超过100%）。
9. Ratio and Direct Proportion | 比与正比例
Example Question: The ratio of adults to children at a show is 5:3. There are 96 people altogether. How many children are there?
例题：一场演出中成人与儿童的人数比是 5:3。总共有96人。请问有多少名儿童？
le = 96, so 1 part = 96 ÷ 8 = 12. Children correspond to 3 parts, so 3 × 12 = 36 children.
比的总份数为 5 + 3 = 8 份。总人数96，所以每份为 96 ÷ 8 = 12。儿童占3份，因此 3 × 12 = 36 名儿童。
Common error: Reversing the ratio, giving children 5 parts and adults 3 parts. Always label which number corresponds to which group.
常见错误：把比的前后项弄反，儿童算成5份，成人3份。务必标注清楚每个数字对应哪一组。
For proportion problems like ‘If 4 pens cost £1.20, how much do 7 pens cost?’, find the unit cost first: £1.20 ÷ 4 = £0.30, then 7 × £0.30 = £2.10.
对于如“4支笔1.20英镑，7支笔多少？”的正比例问题，先求单价：1.20 ÷ 4 = 0.30英镑，再乘7：0.30 × 7 = 2.10英镑。
10. Number Patterns and Sequences | 数列规律
Example Question: Write the next two terms and the nth term rule for the sequence: 3, 7, 11, 15, ...
例题：写出数列 3, 7, 11, 15, … 的后两项以及第 n 项的表达式。
19 and 23. For nth term: start with 4n. When n=1, 4×1 = 4, but first term is 3, so we need –1. The rule is 4n – 1.
相邻两项的差恒为 +4。后两项为 19 和 23。第 n 项：从 4n 开始。当 n=1，4×1=4，而首项是 3，故需 –1。表达式为 4n – 1。
Check for n=2: 4×2 – 1 = 7, which matches the second term. Always test your rule on at least two positions.
验证 n=2：4×2 – 1 = 7，与第二项相符。至少用两个位置检验你的通项公式。
If the difference changes, the sequence may be quadratic. For Year 7, focus on linear patterns. Recognise also patterns like squares (1, 4, 9, 16…) and cubes.
如果差在变化，可能是二次数列。7年级主要集中在一次线性规律。也要认识平方数（1, 4, 9, 16…）和立方数模式。
11. Time and Money Calculations | 时间与金钱计算
Example Question: A film starts at 14:35 and ends at 17:10. How long is the film in hours and minutes?
例题：一部电影从14:35开始，17:10结束。电影时长是多少小时和分钟？
From 17:00 to 17:10 is 10 minutes. Total: 2 hours + 25 min + 10 min = 2 hours 35 minutes.
从14:35到15:00是25分钟，从15:00到17:00是2小时，从17:00到17:10是10分钟。总计：2小时 + 25分 + 10分 = 2小时35分钟。
Alternatively, use subtraction: 17:10 – 14:35. Borrow 1 hour (60 min): 16:70 – 14:35 = 2 hours 35 minutes. Be careful when crossing the hour mark.
也可直接用减法：17:10 – 14:35。借1小时作60分钟：16:70 – 14:35 = 2小时35分钟。跨小时时要格外小心。
In money questions, always give answers with the £ or p symbol, and use two decimal places for pounds: £4.5 should be written as £4.50. Rounding incorrectly loses marks.
在金钱题目中，答案必须带 £ 或 p 符号，英镑保留两位小数，如 £4.5 应写成 £4.50。四舍五入错误会丢分。
12. Exam Technique and Avoiding Common Pitfalls | 考试技巧与避开常见陷阱
Top tip 1: Read every question twice. Underline key words such as ‘not’, ‘estimate’, ‘show your working’. Many marks are lost simply by misreading what is being asked.
首要技巧一：每道题读两遍。圈出关键词，如“不”“估算”“写出过程”。许多失分只是因为误读了题目要求。
Top tip 2: Show all working clearly. Even if your final answer is wrong, you can earn method marks. On the Cambridge paper, marks are awarded for correct steps, not just the answer.
首要技巧二：清晰展示所有步骤。哪怕最终答案有误，过程也能得分。剑桥试卷会为正确的解题步骤给分，而非仅看答案。
Top tip 3: Check units. If a question gives measurements in cm but asks for the answer in metres, convert early. A common error is writing the perimeter of a 5 cm by 8 cm rectangle as 26 cm²—confusing perimeter with area.
首要技巧三：检查单位。若题目给出厘米但要求以米作答，尽早换算。常见错误是将长5cm宽8cm的矩形周长写成26 cm²——混淆了周长和面积。
Top tip 4: Manage your time. Usually you have about 1.5 minutes per mark. Don’t spend 10 minutes on a 2‑mark question. Move on and return later if possible.
首要技巧四：管理时间。通常每分对应1.5分钟。不要在2分的题目上花费10分钟。跳过并稍后再回来。
Finally, always review your answers if time allows, paying special attention to calculation checks, negative signs, and fraction simplifications.
最后，如果时间允许，务必检查答案，特别关注计算校验、负号以及分数的化简。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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